When you behead a word, you remove the first letter and still have a valid word. You will be given clues for the two words, longer word first.
Example: Begin -> Sour, acidic
Answer: The words are Start and Tart.

Nice teaser; I very much enjoyed it. I had to give the most thought to number four - I kept wanting to start with the word "rise", but the right answer finally came to me! I look forward to more like this one.